Two variable gain amplifiers (VGAs) that adopt new approximated exponential equations are proposed in this paper. The dB-linear range of the proposed VGAs is extended more than what the approximated exponential equations predict by a bias circuit technique that adopts negative feedback. The proposed VGAs feature wide gain variation, low-power, high linearity, wide control signal range, and small chip size. One of the proposed VGAs is fabricated in 0.18μm CMOS technology and measurements show a gain variation of 83dB (-36-47dB) with a gain error of less than ±2dB, and P1dB/IIP3 from -55/8 to -20/20.5dBm, while consuming an average current of 3.4mA from a 1.8V supply; the chip occupies 0.4mm2. The other VGA is simulated in 0.18μm CMOS technology and simulations show a gain variation of 91dB (-41-50dB), and P1dB/IIP3 from -50/-25 to -33/0dBm, while consuming an average current of 1.5mA from a 1.8V supply.